Let us briefly observe that assuming \(\varphi (c)=c^\sigma \)  allows to cover several existing models of random walks on hypergraphs.
For \(\sigma =1\) , we get the random walk defined in [1]}, while for \(\sigma =-1\)  we obtain the one introduced by Zhou [2]}. Finally, the case \(\sigma =0\)  returns a random walk on
the so called clique reduced multigraph. The latter is a multigraph
where each pair of nodes is connected by a number of edges equal to the number of hyperedges containing that pair in the hypergraph.
